Here is the full list of all 14 LA Cops trophies - there are 2 bronze, 1 silver, 10 gold and 1 platinum.
Only the best of the best earn the right to wear a platinum cop badge.
Kill 100 criminals.
Kill 200 criminals.
Kill 400 criminals.
Kill 600 criminals.
Kill 1000 criminals.
Arrest all criminals in any level.
Complete all the game missions in normal mode.
Complete all 8 main story missions.
Complete all the game missions in Hardcore Mode.
Fully upgrade a Cop and purchase all weapons.
Complete all the game missions in Nightmare Mode.
Finish any level without losing any Cops.
Finish a level without any of your Cops getting hit.